Frailty model for multiple repairable systems hierarchically represented in serial/parallel structures under assumption of ARAm imperfect repairs

Abstract

The main objective of this thesis is to extend the methodology used to treat failure time data. In particular, we wish to propose an appropriate modeling to a context of hierarchically represented repairable systems, subject to competitive risks and unobserved heterogeneity. To do that, we took one of the necessary steps, we propose modeling for a single repairable system with a hierarchical structure under the assumption that the failures follow a non-homogeneous Poisson process with a power-law intensity function under the frequentist and bayesian framework. In this context we used a corrective approach to remove bias with order O(1/n), and the respective exact confidence intervals are proposed. We illustrate the use of both methods with an early-stage real project related to the traction system of an in-pipe robot. In the sequence, we introduced a framework to the reliability estimation in systems with serial structure and failure modes structured in a parallel way, we continued the studies of the robotic unit previously analyzed. Finally, we propose a statistical model to the reliability estimation of groups of repairable systems hierarchically represented, under a competing risks framework, with the consideration of the existence of unobserved heterogeneity that acts individually on the systems of each group, and also the possibility of imperfect repairs. To illustrate, we consider a database with the failures of agricultural machines categorized in different groups.